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 },
 "distance": {
  "d": 27,
  "X": {
   "value": 27,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-10-30",
    "found_at_samples": 300000000,
    "survived_samples": 300000000,
    "tool": "verify/ris_gpu.py (Perlmutter A100)",
    "seeds": [
     1
    ]
   }
  },
  "Z": {
   "value": 27,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-10-30",
    "found_at_samples": 300000000,
    "survived_samples": 300000000,
    "tool": "verify/ris_gpu.py (Perlmutter A100)",
    "seeds": [
     1
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Two-block group-algebra code on the dihedral group D_69 (order 138, n = 276): mul, _ = research/kit/group_algebra.dihedral(69); H_X, H_Z = group_algebra.build_2bga(mul, a=[95, 79, 84, 75], b=[60, 122, 54, 113]), with a and b indices into that element list, H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T].",
  "references": [
   "H.-K. Lin and L. P. Pryadko, Quantum two-block group algebra codes, Phys. Rev. A 109, 022407 (2024), arXiv:2306.16400"
  ],
  "date": "2026-10-24",
  "notes": "Unattended loop run on Perlmutter, iteration 609, direction dihedral-w4, seed 20261626. The loop gate's 8,000-trial search read d = 30; the deeper rungs recorded in notes/ read 27, and the document carries those witnesses.",
  "model": "Claude Fable 5.1 (Claude Code) working for @vprusso",
  "origin": "submission",
  "search_budget": {
   "candidates_screened": 33240,
   "tool": "research/kit/search.screen_adaptive; verify/heuristic_distance.estimate; verify/ris_gpu.py",
   "notes": "candidates_screened counts direction dihedral-w4 of the loop through 29 October; the loop's 390.6 CPU hours cover all five directions",
   "gpu_hours": 0.34,
   "ris_trials_per_side": 300000000
  }
 },
 "family": "generalized-bicycle"
}
